Recent bounds from modular bootstrap [1]}, [2]}, [3]} indicate that at large \(c\) , the lightest non-vacuum primary has an upper bound \(\frac{c+\bar{c}}{12}\) . Using the AdS/CFT dictionary this bound translates to \(1/4G_{N}\)  which is the mass of the lightest blackhole. This indicates that incorporating corrections from low lying \(\vert \chi \rangle \)  states might be same as considering light matter in the bulk along with gravity.
